Electronic Collective Modes in Twisted Bilayer Graphene

Twisted Bilayer Graphene (TBLG) is a structure composed of two graphene sheets stacked with a relative twist angle between them. Cao et al. [Nature 556, 43 (2018)] reported the discovery of a superconducting state in TBLG at a "magic angle" of about 1.05°. There is no consensus yet on the mechanism that causes this state.
We study electronic collective modes in bilayer graphene at various twist angles with a particular emphasis on low-energy plasmons. The calculation is performed for two band structures: the tight-binding model that displays a long-range periodic Moiré pattern at commensurate twist angles, and the continuum model that allows for the calculation of collective modes at and near the magic angle. We discuss the implications of the electronic collective modes spectrum for superconductivity in twisted bilayer graphene.